Exciton diffusion in energetically disordered organic materials

We implement a simple, continuous, analytical model for exciton hopping in an energetically disordered molecular landscape. The model is parameterized against atomistic and lattice Monte Carlo simulations based on quantum-chemical calculations. It captures the essential physics of exciton diffusion in disordered media at different temperatures and yields a universal scaling law of the diffusion length with the dimensionless disorder parameter given by the ratio of the energetic disorder width to the thermal energy.

Figure 1

(Color online) Top panel: $L_D$ as a function of the standard deviation $\sigma$ of the energy distribution at $T=294\text{K}$. Lines show the equilibrium hopping model including first (straight line) and second (dashed line) nearest neighbors. Symbols are from MC simulations: a cubic lattice morphology with Förster transfer rates and only nearest-neighbor hops (squares) and up to third nearest-neighbor hops (circles); a chain morphology with transfer rates calculated at the quantum-chemical level (triangles up). The inset shows the parametric dependence of $L_D$ on the Förster radius from the equilibrium model (see Eq. (5)) for $\sigma =0.02\text{eV}$ (solid line), 0.04 eV (dotted line), and 0.06 eV (dashed line). Bottom panel: $L_D$ at $T=7\text{K}$ for different excitation energies in a Gaussian density of states (shown not normalized as a dashed line) with $\sigma =0.023\text{eV}$ for the nonequilibrium hopping model (solid line) and the MC simulations with quantum-chemical rates (triangles up). The number of exciton hops $n$ vs time $t$ scaled by the decay time $\tau$ for the nonequilibrium model is shown in the inset.

Figure 2

(Color online) Top panel: Arrhenius plot of $L_D$ for the equilibrium hopping model (straight line) and the cubic lattice MC simulations with Förster transfer rates for $\sigma$ in eV of (circles), 0.02 (squares), 0.03 (diamonds), 0.05 (up triangles), 0.06 (sideways triangles), 0.08 (down triangles), and 0.1 (crosses). Dashed lines represent the Arrhenius fit to the MC results at high $T$. Bottom panel: $L_D$ variation with the dimensionless disorder parameter $\sigma /kT$. Symbols are as for the top panel and $\sigma$ in eV of 0.07 (plus signs), and 0.09 eV (asterisks).